Part 1: Background - Graphing

Transcription

1 Department of Physics and Geology Graphing Astronomy 1401 Equipment Needed Qty Computer with Data Studio Software Graphing Part 1: Background - Graphing In science it is very important to find and understand the relationships between variables. Using tables and graphs are just two ways that we can represent data to clearly show interrelationships. A graph is simply a picture of the collected data from some experiment or other source. It is a visual presentation in which trends and relationships between data sets may be made clear. There are many different types of graphs. The most common forms of graphs include bar and pie charts and linear graphs. Below you can find examples of these graphs. Some types of results are generally best shown through a particular form. Historical data, such as the population of Hidalgo County, might be best shown as a bar graph, while the speed of a car might be better shown as a linear graph. Throughout the semester you will make many linear graphs. a. Bar Graph b. Pie Graph 1 c. Linear Graph A linear graph shows how one quantity varies as a second quantity is changed. These are called the dependent and independent variables respectively. Traditionally the independent variable is plotted along the horizontal axis (also known as x-axis), called the abscissa, while the dependent variable goes on the vertical axis (also known as y-axis), called the ordinate. The intersection of the two axes is called the origin and is usually the point of zero value for each variable. The graph itself is the line drawn through (or near) the data points showing the relationship between the two variables in a visual form. 1

2 The following is a list of rules for drawing a graph. 1. Select a title for the graph which tells what the graph represents. 2. Select a scale for each of the axes. These scales should be chosen so that the data can all be plotted on the page and that the graph will fill as much of the page as possible. Selecting the proper scale will make it easier to locate points. The scale must be laid off uniformly along the axes, but each axis can have a different scale. 3. Label each axis. Tell what each scale represents, including the units of measurement. 4. Carefully plot each of the data points by placing a small dot at the intersection of the ordinate and abscissa corresponding to the values of the variables. Draw a small circle around the dot. 5. After all the data has been plotted, join the dots with a smooth curve. This may be a straight line. The curve might not pass through all of the points plotted. We expect some error in our data and the fact that the curve may not pass through all the points may be an indication that there is some error in our data. The curve should come as close to as many points as possible. This is especially required when the data points are to be fit with a straight line. Use a clear p. 2

3 ruler (for a straight line) and make the line pass as near as practical to each data point. DO NOT use just the first and last point; they are no better or worse than the others. The slope of a linear graph can be easily found. The slope can be found by drawing a right-triangle that has the line as its hypotenuse. The height of the triangle is called the rise and the base is called the run. Note that the units of the slope are those of the rise divided by the run. When a graph is a straight line, we say they have a linear relation. It means that the Y variable is directly proportional to the X variable (plus a constant which may be non-zero). The equation of the line in a graph with a linear relation can be written as y = m * x + b where m is known as the slope of the graph and b is known as the y-intercept. There are potentially two intercepts with the axes on every straight-line graph. The x-intercept is where the line crosses the x-axis and the y-intercept is where the line crosses the y-axis. p. 3

4 SAFETY REMINDER Follow the directions for using the equipment. Part 2: Lab Activity Graphing The purpose of this laboratory activity is to introduce the student to graphing Graph 1 Using the graph paper provided in the lab report, create a simple linear graph. Make sure it contains all the parts mentioned in the lab. <Y variable vs. X variable> X variable [unit x] Y variable [unit y] Graph 2 Using the procedure below, create a simple linear graph using Datastudio <Length vs. Force> x-axis Force (N) y-axis Length (cm) Find the slope and y-intercept and write the equation of the line in the lab report section. PART B I: Computer Setup 1. Start the DataStudio software 2. Once the software starts up, a screen similar to the one pictured here will appear. Select Enter Data. PART B II: Entering Data Table 1. Two windows will appear as shown on the right. On the right side of the screen will be the Data Table window, and on the left will be the graph area. Using the data table above, enter the x and y pairs to be graphed. You will notice that as you enter the data into the data table, the points will begin to appear on the graph, and the scales will automatically adjust to make p. 4

5 the graph take up as much space on the window as possible. 2. Click Summary ( ) in the top of the screen. A window will appear on the left of the data table. 3. Add the title to your graph. In the Displays ( )section of the window on the left, click on Graph 1 and change it to what you want the title of your graph to be. 4. Add the label and units for each axis. In the Data section ( ) of the window on the left, double click on Data. A new window will open. In this new window select the General tab. Change the variable name from x to what your label for the x axis is, and under units type in the units for this same axis. In the drop down menu of the variable name select Y and replace Y with your label for the y axis of your graph, and under units type in the units for this same axis. 5. Click Summary in the top of the screen to remove the left window. PART B III: Analyzing the Data 1. Click Fit ( ) in the Graph toolbar and select Linear. This will draw the linear fit line and a text box will appear on the graph with the y intercept and slope automatically calculated by the computer. Record the slope and y intercept in the lab report section. 2. Using the slope and y intercept from the computer, find the equation of the line and record it in the lab report section. 3. Print a copy of the graph and attach it to the lab report section Graph 3 Using the procedure above, create a simple linear graph <Distance vs. Time> X axis Time [sec] Y axis Distance [cm] Find the slope and y-intercept and write the equation of the line in the lab report section. 2.2 Slopes Find the slope of the indicated segments of the figure in section 3.2 MAKE SURE TO ATTACH YOUR GRAPHS TO YOUR LAB REPORT p. 5

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